Context. Deuteration is a powerful tracer of the history of the cold prestellar phase in star-forming regions. Apart from methanol, little is known about deuterium fractionation of complex organic molecules in the interstellar medium, especially in regions forming high-mass stars. Aims. Our goal is to detect deuterated complex organic molecules toward the high mass star-forming region Sagittarius B2 (Sgr B2) and derive the level of deuteration for these molecules. Methods. We use a complete 3-mm spectral line survey performed with the Atacama Large Millimeter/submillimeter Array (ALMA) to search for deuterated complex organic molecules toward the hot molecular core Sgr B2(N2). We constructed population diagrams and integrated intensity maps to fit rotational temperatures and emission sizes for each molecule. Column densities are derived by modeling the full spectrum under the assumption of local thermodynamic equilibrium. We compare the results to predictions of two astrochemical models that treat the deuteration process. Results. We report the detection of CH 2 DCN toward Sgr B2(N2) with a deuteration level of 0.4%, and tentative detections of CH 2 DOH, CH 2 DCH 2 CN, the chiral molecule CH 3 CHDCN, and DC 3 N with levels in the range 0.05%-0.12%. A stringent deuteration upper limit is obtained for CH 3 OD (<0.07%). Upper limits in the range 0.5-1.8% are derived for the three deuterated isotopologues of vinyl cyanide, the four deuterated species of ethanol, and CH 2 DOCHO. Ethyl cyanide is less deuterated than methyl cyanide by at least a factor five. The [CH 2 DOH]/[CH 3 OD] abundance ratio is higher than 1.8. It may still be consistent with the value obtained in Orion KL. Except for methyl cyanide, the measured deuteration levels lie at least a factor four below the predictions of current astrochemical models. The deuteration levels in Sgr B2(N2) are also lower than in Orion KL by a factor of a few up to a factor ten. Conclusions. The discrepancy between the deuteration levels of Sgr B2(N2) and the predictions of chemical models, and the difference between Sgr B2(N2) and Orion KL may both be due to the higher kinetic temperatures that characterize the Galactic center region compared to nearby clouds. Alternatively, they may result from a lower overall abundance of deuterium itself in the Galactic center region by up to a factor ten.